Chemistry in Lasers. XI. Non-Classical Aspects of Fusion: The Zhabotinsky Effect and Communications Theory

Developed from the application of operational mathematics and Markoff-theory in quantum mechanics [CA: 81: 8225v], transform space treatment of Einstein diffusion [CA: 82: 49699s], and acoustoopic effects in lasers [CA: 82: 162686y], the paper examines non-classical aspects of laser driven fusion presenting favorable options which remain generally inexplored.     

A vertex-face assignment for plane graphs

For every planar straight line graph (Pslg), there is a vertex-face assignment such that every vertex is assigned to at most two incident faces, and every face is assigned to all its reflex corners and one more incident vertex. Such an assignment allows us to augment every disconnected Pslg into a connected Pslg such that the degree of every vertex increases by at most two.     

Detecting “dense” columns in interior point methods for linear programs

During the iterations of interior point methods symmetric indefinite systems are decomposed by LD̂L ^T factorization. This step can be performed in a special way where the symmetric indefinite system is transformed to a positive definite one, called the normal equations system. This approach proved to be efficient in most of the cases and numerically reliable, due to the positive definite property. It has been recognized, however, that in case the linear program contains “dense” columns, this approach results in an undesirable fill–in during the computations and the direct factorization of the symmetric indefinite system is more advantageous. The paper describes a new approach to detect cases where the system of normal equations is not preferable for interior point methods and presents a new algorithm for detecting the set of columns which is responsible for the excessive fill–in in the matrix AA ^T . By solving large–scale linear programming problems we demonstrate that our heuristic is reliable in practice. This work was supported in part by the Hungarian Scientific Research Fund OTKA K60480.     

An Improved Esterification of Carboxylic Acids Using Phase Transfer Conditions Without Solvents

Esterification of sodium salt of carboxilic acids were performed with alkyl bromide in phase-transfer conditions without solvent.     

A Mild Method for the Formation of Tosylhydrazone Derivatives from Keto Esters

An improved preparation of tosylhydrazones of α- and β-keto esters, by means of active aluminium oxide as catalyst, are described.     

Enzyme-catalyzed synthesis of (R)- and (S)-3-hydroxy-3-(10-alkyl-10H-phenothiazin-3-yl)propanoic acids

Starting from the racemic ethyl 3-hydroxy-3-(10-alkyl-10H-phenothiazin-3-yl)propanoates as substrates, a multienzymatic procedure was developed for the efficient synthesis of the corresponding highly enantiomerically enriched (R)- and (S)-3-heteroaryl-3-hydroxypropanoic acids.     

Applying oracles of on-demand accuracy in two-stage stochastic programming – A computational study

Traditionally, two variants of the L-shaped method based on Benders’ decomposition principle are used to solve two-stage stochastic programming problems: the aggregate and the disaggregate version. In this study we report our experiments with a special convex programming method applied to the aggregate master problem. The convex programming method is of the type that uses an oracle with on-demand accuracy. We use a special form which, when applied to two-stage stochastic programming problems, is shown to integrate the advantages of the traditional variants while avoiding their disadvantages. On a set of 105 test problems, we compare and analyze parallel implementations of regularized and unregularized versions of the algorithms. The results indicate that solution times are significantly shortened by applying the concept of on-demand accuracy.     

Art gallery problem with guards whose range of vision is 180

It is shown that in any polygonal art gallery of n sides it is possible to place n/3 point guards whose range of vision is 180° so that every interior point of the gallery can be seen by at least one of them. The guards can be stationed at any point of the art gallery. This settles an open problem posed by J. Urrutia.